The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  2  1  1  1  1  1  1  1  1  1  2  4  1  1  1  1  4  1  1  1  1
 0 12  0 12  0 12  0  4  8 12  0 12  0 12  4 12  8 12  4  0  8  0  8 12 12 12 12  4  4 12  4 12  0  0
 0  0  8  0  0  0  0  0  8  0  0  0  8  8  0  0  8  8  8  0  8  8  0  0  0  0  8  8  8  8  0  8  0  0
 0  0  0  8  0  0  0  8  0  0  0  8  0  8  8  0  0  8  8  8  8  8  8  0  8  0  0  0  0  8  0  0  8  0
 0  0  0  0  8  0  0  0  0  8  8  8  0  8  0  8  8  0  8  8  8  0  8  0  8  8  8  0  0  0  0  0  8  8
 0  0  0  0  0  8  0  8  0  8  8  0  8  8  0  0  0  8  0  0  8  0  8  0  8  0  8  8  8  0  8  0  0  0
 0  0  0  0  0  0  8  0  8  0  8  8  0  0  8  0  8  8  8  0  8  8  0  0  8  8  8  0  8  0  8  0  8  0

generates a code of length 34 over Z16 who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+42x^28+96x^30+348x^32+1088x^34+334x^36+96x^38+34x^40+7x^44+1x^48+1x^60

The gray image is a code over GF(2) with n=272, k=11 and d=112.
This code was found by Heurico 1.16 in 0.0709 seconds.